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Jennings-Shaffer, Chris and Reihill, Dillon (2020). Asymptotic formulas related to the M-2-rank of partitions without repeated odd parts. Ramanujan J., 52 (1). S. 175 - 243. DORDRECHT: SPRINGER. ISSN 1572-9303

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Abstract

We give asymptotic expansions for the moments of the M-2-rank generating function and for the M-2-rank generating function at roots of unity. For this we apply the Hardy-Ramanujan circle method extended to mock modular forms. Our formulas for the M-2-rank at roots of unity lead to asymptotics for certain combinations of N2(r, m, n) (the number of partitions without repeated odd parts of n with M-2-rank congruent to r modulo m). This allows us to deduce inequalities among certain combinations of N2(r, m, n). In particular, we resolve a few conjectured inequalities of Mao.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Jennings-Shaffer, Chris UNSPECIFIED UNSPECIFIED UNSPECIFIED Reihill, Dillon UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-336025
DOI:	10.1007/s11139-019-00147-y
Journal or Publication Title:	Ramanujan J.
Volume:	52
Number:	1
Page Range:	S. 175 - 243
Date:	2020
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9303
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MOCK THETA-FUNCTIONS; COEFFICIENTS; MOMENTS; DYSONS; FORMS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/33602